The vertices of cubic function c(x) are located at (−3,1)
 and (2,−9)
 Where are the vertices of 13c(x)
 located? Enter your responses as ordered pairs. Do not include any spaces.
$$

Given that the vertices of the cubic function $ c(x) $ are located at $ (-3, 1) $ and $ (2, -9) $, we need to determine the vertices of the function $ 13c(x) $.

### Step 1: Understanding the effect of multiplying by 13

When a function $ c(x) $ is scaled by a constant factor $ 13 $, the **x-coordinates of the vertices** remain the same. However, the **y-coordinates** of the vertices are multiplied by 13, as this affects the output (y-values) of the function.

### Step 2: Calculating the new y-coordinates

For the vertex $ (-3, 1) $:
- The x-coordinate remains $ -3 $.
- The new y-coordinate is $ 13 \times 1 = 13 $.

For the vertex $ (2, -9) $:
- The x-coordinate remains $ 2 $.
- The new y-coordinate is $ 13 \times (-9) = -117 $.

### Step 3: Writing the new vertices

The vertices of the function $ 13c(x) $ are:
- $ (-3, 13) $
- $ (2, -117) $

Thus, the vertices are located at $ (-3,13) $ and $ (2,-117) $.

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Would you like further explanation or have any questions about this solution?

Here are some related questions:
1. What happens to the roots of a cubic function when multiplied by a constant?
2. How do the x-intercepts change when scaling a function vertically?
3. What is the geometric interpretation of multiplying a function by a constant?
4. Can we generalize this process for quadratic or other polynomial functions?
5. How would adding a constant to $ c(x) $ affect the vertices?

**Tip**: Scaling a function vertically does not affect the x-coordinates of special points like vertices, only the y-values.

The vertices of cubic function c(x) are located at (-3,1) and (2,-9). Where are the vertices of 13c(x) located? Enter your responses as ordered pairs. Do not include any spaces.

Explore how to find the vertices of a scaled cubic function. Given the vertices of the original cubic function c(x) as (-3,1) and (2,-9), learn how vertical scaling by 13 affects the function's y-values, resulting in the new vertices (-3,13) and (2,-117). Suitable for students in Grades 9-12.

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